(x-2)(x+5)=(x-3)(x+8)

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Solution for (x-2)(x+5)=(x-3)(x+8) equation: 


Simplifying
(x + -2)(x + 5) = (x + -3)(x + 8)

Reorder the terms:
(-2 + x)(x + 5) = (x + -3)(x + 8)

Reorder the terms:
(-2 + x)(5 + x) = (x + -3)(x + 8)

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) = (x + -3)(x + 8)
((5 * -2 + x * -2) + x(5 + x)) = (x + -3)(x + 8)
((-10 + -2x) + x(5 + x)) = (x + -3)(x + 8)
(-10 + -2x + (5 * x + x * x)) = (x + -3)(x + 8)
(-10 + -2x + (5x + x2)) = (x + -3)(x + 8)

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) = (x + -3)(x + 8)

Reorder the terms:
-10 + 3x + x2 = (-3 + x)(x + 8)

Reorder the terms:
-10 + 3x + x2 = (-3 + x)(8 + x)

Multiply (-3 + x) * (8 + x)
-10 + 3x + x2 = (-3(8 + x) + x(8 + x))
-10 + 3x + x2 = ((8 * -3 + x * -3) + x(8 + x))
-10 + 3x + x2 = ((-24 + -3x) + x(8 + x))
-10 + 3x + x2 = (-24 + -3x + (8 * x + x * x))
-10 + 3x + x2 = (-24 + -3x + (8x + x2))

Combine like terms: -3x + 8x = 5x
-10 + 3x + x2 = (-24 + 5x + x2)

Add '-1x2' to each side of the equation.
-10 + 3x + x2 + -1x2 = -24 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x + 0 = -24 + 5x + x2 + -1x2
-10 + 3x = -24 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x = -24 + 5x + 0
-10 + 3x = -24 + 5x

Solving
-10 + 3x = -24 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.
-10 + 3x + -5x = -24 + 5x + -5x

Combine like terms: 3x + -5x = -2x
-10 + -2x = -24 + 5x + -5x

Combine like terms: 5x + -5x = 0
-10 + -2x = -24 + 0
-10 + -2x = -24

Add '10' to each side of the equation.
-10 + 10 + -2x = -24 + 10

Combine like terms: -10 + 10 = 0
0 + -2x = -24 + 10
-2x = -24 + 10

Combine like terms: -24 + 10 = -14
-2x = -14

Divide each side by '-2'.
x = 7

Simplifying
x = 7

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